The equation of spacetime motion of a point charge under the action of an external force is an old problem of electromagnetism.
The original work of Abraham (treated e.g. in [1]}, Ch. 16.3) and then Dirac's formulation
(treated e.g. in [2]}, Ch III.3) suffers from a hardly acceptable mass renormalization according to which the finite
mass of a particle is the difference of the positive infinite electric mass and the negative infinite mechanical mass. Other,
quick deductions based on Larmor's formula and some other `natural' requirements (see [1]},
Ch 16.2) are not convincing either.
Moreover, the LAD equation admits physically untenable run-away solutions.
There are some attmepts to exclude such non-physical solutions by imposing extra conditions.
(e.g. [4]}, [5]}).
There are a number of articles (e.g.[6]}, [7]}, [8]},
[9]}, [10]}) considering various continuum charge distributions
instead of a point charge and then taking or not the limit to a point.
Though casting more and more new light on the problem and its possible solution, neither way seems
satsifactory.
